Refined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions
Analysis of PDEs
2011-10-31 v1
Abstract
The nonnegative viscosity solutions to the infinite heat equation with homogeneous Dirichlet boundary conditions are shown to converge as time increases to infinity to a uniquely determined limit after a suitable time rescaling. The proof relies on the half-relaxed limits technique as well as interior positivity estimates and boundary estimates. The expansion of the support is also studied.
Keywords
Cite
@article{arxiv.1004.4418,
title = {Refined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions},
author = {Philippe Laurencot and Christian Stinner},
journal= {arXiv preprint arXiv:1004.4418},
year = {2011}
}